Shape Of Membership Functions Research Articles

Precision contouring control of five degree of freedom robot manipulators with uncertainty

In this article, we apply a result in equivalent errors to a contouring control problem of five degree of freedom robot manipulators. The proposed technique, fuzzy Proportional Integral Derivative (PID) with the robust extended Kalman filter, is employed to stabilize the dynamic of equivalent errors of robot manipulators. The shape of membership functions and rules of fuzzy PID controller are tuned following operating conditions that make the control performance to improve significantly. A desired path in terms of the position of the end-effector of the robot manipulators is described in generalized coordinates defined by the dynamic of equivalent. The simulation and experimental results demonstrate the excellent performance of the proposed technique.

Membership Functions for Fuzzy Focal Elements

Abstract The paper presents a study on data-driven diagnostic rules, which are easy to interpret by human experts. To this end, the Dempster-Shafer theory extended for fuzzy focal elements is used. Premises of the rules (fuzzy focal elements) are provided by membership functions which shapes are changing according to input symptoms. The main aim of the present study is to evaluate common membership function shapes and to introduce a rule elimination algorithm. Proposed methods are first illustrated with the popular Iris data set. Next experiments with five medical benchmark databases are performed. Results of the experiments show that various membership function shapes provide different inference efficiency but the extracted rule sets are close to each other. Thus indications for determining rules with possible heuristic interpretation can be formulated.

Fuzzy Reliability Theory Based on Membership Function

In this study, it is considered that the shape of membership function and the values of parameters are arbitrary, hence reliability parameters will be arbitrary, and some data are even absurd from the point of view of real life practice. An applied fuzzy reliability theory is applied to practical engineering problem. Method of fuzzy reliability evaluation are developed.

A Comparative Analysis of Fuzzy Based Hybrid Anfis Controller for Stabilization and Control of Nonlinear Systems

This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters of the IP system. The results shows that ANFIS controller provides better results in comparison to both fuzzy controller.

Adaptive Neuro-Fuzzy Inference Systems as a Strategy for Predicting and Controling the Energy Produced from Renewable Sources

The challenge for our paper consists in controlling the performance of the future state of a microgrid with energy produced from renewable energy sources. The added value of this proposal consists in identifying the most used criteria, related to each modeling step, able to lead us to an optimal neural network forecasting tool. In order to underline the effects of users’ decision making on the forecasting performance, in the second part of the article, two Adaptive Neuro-Fuzzy Inference System (ANFIS) models are tested and evaluated. Several scenarios are built by changing: the prediction time horizon (Scenario 1) and the shape of membership functions (Scenario 2).

A GA-Based Adaptive Neuro-Fuzzy Controller for Greenhouse Climate Control System

In this research paper, a new application of Adaptive Neuro-Fuzzy Inference System (ANFIS) to the control of greenhouse climate system is introduced. To cope with the large amount of uncertainties present in such systems and in order to improve the system performance, a Genetic Algorithm (GA) is used to adapt the controller parameters such as the number and shape of membership functions employed and scaling factors. Simulation results showed that the proposed control architecture is able to provide smooth control regardless of the continuously changing environmental conditions and the complexity of the plant. The performance of the proposed controller has been assessed against other traditional controllers and has been found to outperform its counterparts.

A Learning-Based Fault Tolerant Tracking Control of an Unmanned Quadrotor Helicopter

This paper presents a novel learning-based fault tolerant tracking control approach by using an extended Kalman filter (EKF) to optimize a Mamdani fuzzy state-feedback tracking controller. First, a robust state-feedback tracking controller is designed as the baseline controller to guarantee the expected system performance in the fault-free condition. Then, the EKF is employed to regulate the shape of membership functions and rules of fuzzy controller to adapt with the working conditions automatically after the occurrence of actuator faults. Next, based on the modified fuzzy membership functions and rules, the baseline controller is readjusted to properly compensate the adverse effects of actuator faults and asymptotically stabilize the closed-loop system. Finally, in order to verify the effectiveness of the proposed method, several groups of numerical simulations are carried out by comparing the performance of a tracking control scheme and the presented technique. Simulation results demonstrate that the proposed method is effective for optimizing the fuzzy tracking controller on-line and counteracting the side effects of actuator faults, and the control performance is significantly improved as well.

Enhanced approximation capabilities of the fuzzy systems using variable universes of discourse

The fuzzy systems with variable universe of discourse (VUD) have received increasing attention due to their fine control performance. VUD fuzzy systems are ones in which universes of discourse can be online tuned by means of a set of nonlinear contraction–expansion factors. One advantage of the VUD fuzzy systems lies in that higher control accuracy can be obtained without the aid of integral elements. Another advantage of the VUD fuzzy systems is that the number of fuzzy rules can be reduced significantly for a given application, compared with the fuzzy system based on fixed universes of discourse. Utilizing the multivariable Taylor’s expansion formula, it is proven that the VUD fuzzy system possesses higher approximating power as the input variables approach the equilibrium point. The approximation error converges to zero when the input variables reach the equilibrium point. It is also proven that the same approximating power can be obtained even when two fuzzy sets are applied on any universe of discourse. In addition, a sufficient condition is given for the VUD fuzzy systems as approximators for any given accuracy. Two examples show that the approximating capability of the VUD fuzzy systems can significantly outperform the fuzzy systems with fixed universes of discourse and that the shape of membership functions can influence the approximation effect. This paper provides researchers with some explanations why the VUD fuzzy systems hold the two advantages mentioned above from the standpoint of the functions approximation theories.

Application of Fuzzy Logic for Decision-Making in Medical Expert Systems

For certain problems of predictive medicine, early and differential diagnosis in construction of relevant expert systems are best solved using methods of fuzzy decision-making adapted to classification problems. For selection of shape and parameters of membership functions of studied classes of states and methods of their aggregation, the use of the methodology of exploratory analysis followed by unification of particular decision rules into fuzzy groups that provide the best quality of classification is proposed. Recommendations are given for the synthesis of partial fuzzy decision rules and their groups to build a knowledge base of medical expert systems.

An ensemble neuro-fuzzy radial basis network with self-adaptive swarm based supervisor and negative correlation for modeling automotive engine coldstart hydrocarbon emissions: A soft solution to a crucial automotive problem

In this paper, the authors propose a novel intelligent framework to identify the exhaust gas temperature (Texh) and the engine-out hydrocarbon emission (HCraw) during the coldstart operation of an automotive engine. These are two key variables affecting the cumulative tailpipe emissions (HCcum) over the coldstart phase, which is the number one emission-related problem for today's spark-ignited (SI) engine vehicles. The coldstart operation is regarded as a highly nonlinear, transient and uncertain phenomenon. The proposed identifier integrates different soft computational strategies, i.e. neuro-fuzzy computing, fuzzy controller, swarm intelligent computing, and ensemble network design, beneficial for capturing both uncertainty and nonlinearity of the problem at hand. Furthermore, concepts of negative correlation topology design and hierarchical pair competition based parallel training are extracted from literature to form a diverse and robust ensemble identifier. Training of each neuro-fuzzy sub-component in ensemble network is carried out using a hybrid learning scheme. One feature of the antecedent part of neuro-fuzzy system, i.e. number of linguistic terms for each variable, as well as characteristics of rules in rule base are adjusted using hierarchical fair competition-based parallel adaptive particle swarm optimization (HFC-APSO) and the rest of features, i.e. the shape of (membership functions) MFs and the consequent variables of each rule, are tuned using back-propagation (BP) and steepest descent techniques. As it was mentioned, the authors try to design an ensemble identifier with acceptable rate of generalization, robustness and accuracy. These features help them to tame the intuitive uncertainties associated with the rate of Texh and HCraw emission over the coldstart period. To do so, the potential characteristics of sub-components (solution domain of network design) are divided into a set of partitions and then HFC-APSO is utilized to explore/exploit each of those partitions. The exploration/exploitation rate of PSO (the core of HFC-APSO) is dynamically controlled by a fuzzy logic based controller. Hence, it is expected that HFC-APSO yields a set of accurate sub-identifiers with different operating characteristics. To further foster the diversity of the ensemble, negative correlation criterion is considered which obstructs the integration of identical sub-identifiers. The identification results demonstrate that the method is highly capable of providing an authentic model for estimation of Texh and HCraw emission during the coldstart period.

A comparison of membership function shapes in a fuzzy-based fugacity model for disinfection byproducts in indoor swimming pools

Aleatory and epistemic uncertainty in human health risk assessment is virtually unavoidable. While probabilistic methods may adequately address exposure and risk model parameters with variability (body weight, exposure duration, exposure frequency), other methods are more helpful for handling uncertainty that arises from an incomplete understanding of the processes being modeled (mass transport). Due to the potential for cancer and other health risks, it is essential to understand of the concentrations of disinfection byproducts in swimming pool facilities and the related exposures. This study builds on previous probabilistic and fuzzy based fugacity models which estimate exposure to disinfection byproducts in swimming pools (Dyck, Water Res 45:5084–5098, 2011; Annual meeting of the North American Fuzzy Information Processing Society (NAFIPS), 2012). Those models estimated environmental concentrations based on mass transfer processes for which there are many possible formulas. The influence of membership function shape on the final estimated concentration required further investigation. In this study, three different trapezoidal membership functions are derived for the gas-side mass transfer coefficient k G . One triangular and one trapezoidal membership function are derived for the liquid-side mass transfer coefficient, k L . According to graphical output and percent difference between the actual concentration and the defuzzified output of the fuzzy based model, the best combination of shapes to use is the trapezoidal k G membership function which uses seven calculated values (to define the shape of the trapezoid) with either the triangular or trapezoidal k L membership function. Further study is recommended to combine the fuzzy based methods for poorly understood model processes with probabilistic methods for model parameters with aleatory uncertainty.

A weighted CREAM model for maritime human reliability analysis

Human error can be regarded as a significant factor contributing to marine accidents. Crew onboard vessels often perform duties in circumstances where technological, environmental and social factors emerge which may contribute to the occurrence of human failures. Fuzzy Cognitive Reliability and Error Analysis Methods (CREAM) is one of the most recognized HRA methods capable of tackling such difficulties. However, shortcomings are still disclosed and weaken the applicability of such an approach. These include the lack of considering input weights, the dubitation of the logicality of adopting rule base approaches to evaluate the relations between inputs and output and the loss of useful information due to the application of min–max fuzzy inference method. A new fuzzy CREAM methodology capable of resolving the aforementioned difficulties is proposed based on a rule base approach. The framework is validated using two axioms and demonstrated by virtue of an oil tanker example. The results are consistent with the principles evolved from the axioms since the outcomes are sensitive to the minor alterations of input data and weights. It is concluded that the weighted CREAM model is able to produce reliable human performance failure results and the strengths will not be compromised even if applied in circumstances where membership function shapes of fuzzy sets are various from traditional studies.

Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

AbstractIn the present work, efforts are made to develop the input-output relationships for squeeze casting process by utilizing the fuzzy logic based approaches. Casting density in Squeeze casting is expressed as function of process parameters, such as time delay before pressurizing the metal, pressure durations, squeeze pressure, pouring temperature and die temperature. It is to be noted that, Mamdani based model and Takagi and Sugeno's model have been developed to model density in squeeze casting process. Manually constructed Mamdani based fuzzy logic controller and Takagi and Sugeno's based fuzzy logic controller have been used in approach 1 and approach 2 respectively. Training of FLC is carried with the help of five hundred input-output data set generated artificially through regression equations, obtained earlier by the same authors. The performance of the developed models was tested for both the linear and non-linear membership function distributions with the help of ten test cases. Moreover, the test data was collected by conducting the experiments and not used in training of FLCs. It is interesting to note that both approaches are capable to make accurate predictions. However, the performance of approach 2 with G bell shape membership function distribution is found to outperform approach 1 and other type of membership function distributions. The findings are useful to foundry-men, since it provides information on casting density in squeeze casting process for the different combination of process parameters without conducting any experiments.

Structural Damage Detection by Fuzzy Logic Technique

In this paper, a novel approach for detecting crack location and its intensity in cantilever beam by Fuzzy logic techniques is established. The analysis has been done by using ANSYS FE software. The fuzzy controller with Bell shaped membership functions are used here which consists of three input parameters are relative deviation of first three natural frequencies and two output parameters are relative crack depth and relative crack location respectively. A series of fuzzy rules are resulting from vibration parameters which are finally used for prediction of crack location and its intensity. This method provides the knowledge towards the detection, location and characterization of the damage in the cantilever beam.

Programmable Implementation of Diamond-Shaped Type-2 Membership Function in CMOS Technology

In this paper, circuit implementation of diamond-shaped type-2 membership function in CMOS technology is presented. Designing of mixed analog/digital circuits provides a flexible configuration as well as the highly accurate performance, where analog circuits are employed to realize required functions, while the programmable units implemented using digital circuits. The current-mode approach is employed owing to the simple circuitry and intuitive configuration to design the circuits. The programmability of the circuit in terms of slopes, upper, and lower modal points enables the expert of the system to create other shapes of type-2 membership functions including rectangular, rhombus, triangular, and trapezoidal. For a particular set of programming parameters of diamond-shaped type-2 membership function, post layout simulation results of the proposed circuit using HSPICE and level 49 parameters (BSIM3v3) in 0.18 $$\mu $$ μ m technology, demonstrate an average power consumption of 0.688 mW, maximum propagation delay of 8.7 ns and a relative error as low as $$\pm $$ ± 1 %. Furthermore, Monte Carlo analysis is carried out to ensure the robustness of the circuit performance against the process variation.

Real time voltage stabilization in microgrid

Abstract This study suggests a new algorithm based on a combination of fuzzy logic and genetic algorithm (GA) to improve voltage profile in a microgrid. The considered microgrid includes control variables such as onload tap changer (OLTC), active power output from distributed generators (DG) and reactive power output from feeder switched capacitors that are controlled in a microgrid controller (MGC) by communication links. The proposed method was used to obtain the optimum value of control variables to establish voltage stabilization in varying load condition as online. For establishing voltage stabilization at the microgrid, an objective function is defined and is tried to minimize it by control variables. The control variables were changed based on fuzzy logic and the GA was employed for finding the optimum shape of membership functions. In order to verify the proposed method, a 34 buses microgrid in varying load condition was analyzed and was compared with previous works.

Prediction of Tool Life when End Milling of Ti6Al4V Alloy Using Hybrid Learning System

Tool life significantly affects the machining cost and productivity. A wide number of techniques have been applied to modelling metal cutting processes. Techniques of artificial intelligence are new soft computing methods which suit solutions of nonlinear and complex problems such as metal cutting processes. The current study is concerned with the application of an adaptive neuro-fuzzy inference system (ANFIS). This ANFIS model is developed to predict tool life when end milling of Ti6Al4V alloy with coated (PVD) and uncoated cutting tools are under dry cutting conditions. By carrying out training and testing the ANFIS models, the current study employed real experimental results, and based on such results, a selection of the best model was conducted based on the mean absolute percentage error (%). For the modelling process, the study adopted a generalised bell shape membership function, and there was a change in its number from 2 to 5. The findings revealed that ANFIS is capable of modelling tool life in end milling process, and that there was good matching obtained between experimental and predicted results.

THE MULTIMODAL APPROACH TO THE MODELLING OF MODAL SPLIT

Transport in cities plays a crucial role in the lives of inhabitants. Development of cities affects the functional aspects of the network include the emergence of new areas of traffic generators. Unsuited infrastructure causes many negative effects that outraged the standard of living in cities. In this paper the concept of Park and Ride was presented as a way to cope with the growing volume of traffic. Full procedure for estimating the contribution of different modes of transport including the Park and Ride was presented. Additionally, an important part of the article is devoted to a description of full Delphic approach, applied for membership function (MF) shape definition of chosen function, estimating linguistic variable.

Environmental comprehensive assessment of agricultural systems at the farm level using fuzzy logic: A case study in cane farms in Iran

Development of a fuzzy inference model is a complex multi-step process in which we encounter a large number of parameters such as type and number of membership functions, fuzzy operators, defuzzification and implication methods and etc. There is currently very little literature on the topic of the best selection of parameters for development of expert based inference models. In this study we developed a fuzzy rule based model, which uses available farm management data as required inputs, for the environmental assessment of farming systems. We also tried to make an analysis on the efficiency of current mathematical parameters in the development of our fuzzy model. Finally, in a practical example we demonstrate the applicability of the developed model for improvement of environmental status of the cane farming in Iran.A Mamdani fuzzy inference model with two inference engines was developed to combine five basic input indexes, which were selected as indicators of farms environmental status based on the experts' interview and scientific knowledge. To validate the developed model, we inserted several cycles of analysis using graphical and global sensitivity methods on the model and compared the model outcomes with experts' viewpoints. Using these analysis methods, we also evaluated the effects of changes in operators, membership function shape and defuzzification methods, on the model outcomes and their sensitivities.In this study, fuzzy inference emerged as a suitable, uncomplicated and effective tool for development of environmental assessment models. Totally, performance of one parameter was highly influenced by other parameters. For the selection of one parameter its interaction with other parameters had to be considered. Type, shape and the number of membership functions were from the most effective parameters for development of the model and significantly influenced the other factors. Case study results showed that environmental indexes of sugarcane production can enhance between 37 and 59% using simple improving strategies.

Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems With Mismatched Premise Membership Functions

This paper investigates the stability of polynomial-fuzzy-model-based (PFMB) control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. To enhance the design flexibility, the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model, however, which make the stability analysis more difficult and potentially lead to conservative stability analysis result. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is proposed to investigate the stability of the PFMB control systems and synthesize the polynomial fuzzy controller. To facilitate the stability analysis and relax the stability analysis result, the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the SOS-based stability conditions. A simulation example is given to illustrate the effectiveness of the proposed approach.